The Mathematics of Financial Modelingand Investment Management

20-Term Structure Page 612 Wednesday, February 4, 2004 1:33 PM

612 The Mathematics of Financial Modeling and Investment Management

CLASSICAL ECONOMIC THEORIES ABOUT THE

DETERMINANTS OF THE SHAPE OF THE TERM STRUCTURE

As mentioned earlier, the Treasury yield curve shows the relationship

between the yield to maturity on Treasury securities and maturity. His-

torically, three shapes have been observed: an upward sloping yield

curve (the most typical and therefore referred to as a “normal” yield

curve), an downward sloping yield curve (also referred to as an

“inverted” yield curve), and a flat yield curve. Exhibit 20.3 shows the

yield curve for four countries on September 5, 2003 and September 12,

2003: United States, Germany, United Kingdom, and Japan. Notice that

all four yield curves are upward sloping.

While we know that the yield curve is not the same as the term struc-

ture of interest rates, what will the shape of the spot rate curve and short-

term forward rate curve look like? If the yield curve is upward sloping, the

spot rate curve will lie above the yield curve, and the forward rate curve

EXHIBIT 20.3 Global Bellwether Yield Curves, September 5, 2003 and

September 12, 2003